OFDM is a digital multi-carrier modulation method that uses a large number of closely spaced orthogonal sub-carriers to carry data. OFDM is becoming widely applied in wireless communication systems due to the high rate transmission capability with high bandwidth efficiency. Signals received from OFDM transmitting antennas may be subject to channel fading due to multipath propagation or interference between the signals and geographical surroundings. To take account of this, reference signals are mapped onto subcarriers and used at the receiver to obtain channel estimations.
FIG. 1 shows a user equipment (UE) receiver 8 for an OFDM system, which transforms a received radio frequency signal into soft bits representing data. An analog front end 10 amplifies and converts the radio frequency signal, received at multiple receive antennas, from the radio channel frequency to an analog base band signal centered around zero Hz. Multiple antennas are used to achieve receive diversity. This is a 3GPP standard requirement for UE receivers.
A set of analog to digital converters 12 convert the analog baseband signal to a stream of digital samples, with a sampling frequency of 30.72 MHz (a typical example for the 3GPP LTE standard). All subsequent processing after this point is performed in the digital discrete domain. A path searcher and timing tracking block 14 determines the regular points in time where the FFT block 16 starts buffering each set of samples and performs a Fourier transform on them. Processing with the FFT block 16 is a technique required within the LTE and LTE-A standards, as these are both using the OFDM waveform.
The channel estimator 18 provides a set of complex samples, for each OFDM symbol and for each subcarrier, so that the received signal can then be demodulated and converted to soft bits by a demodulator 20. In this example, the demodulator 20 is for a data channel e.g. the physical downlink shared channel (PDSCH). The soft bits that are output from the demodulator 20 are then output to the HARQ and Turbo decoder, which is not shown in FIG. 1. The channel estimator 18 also provides the estimates for a control channel e.g. the physical downlink control channel (PDCCH).
One method of channel estimation is the 2D Linear Minimum Means Square Error (2D LMMSE). In this method, the channel estimator 18 multiples a G matrix by least squares (LS) channel estimates as will be described below.
FIG. 2 shows an example block of OFDM resource elements. The resource element (RE) of frequency time index (ki, li) is indexed i with:i=li×K+ki iεΩ=[0,1, . . . , L×K−1]kiε[0,1, . . . , K−1]liε[0,1, . . . , L−1]  Equation 1-1
The indexing method i=ki×L+li is also possible and has the same results as the method above (i=li×K+ki).
The time frequency correlation between the channels of a transmission link between a transmit point (antenna) and a receive point (antenna) at the m-th RE, hm, and at the n-th RE, hn, is as follows:E{hmhn*}=rj(km−kn)ri(lm−ln), mεΩ, nεΩ.  Equation 1-2
For an exponential power delay profile, the frequency domain correlation between two sub-carriers km and kn is given by:
                                          r            f                    ⁡                      (                                          k                m                            -                              k                n                                      )                          =                  1                      1            +                          j              ⁢                                                          ⁢              2              ⁢              π              ⁢                                                          ⁢                                                τ                  rms                                ⁡                                  (                                                            k                      m                                        -                                          k                      n                                                        )                                            ⁢              Δ              ⁢                                                          ⁢              f                                                          Equation        ⁢                                  ⁢        1        ⁢                  -                ⁢        3            where Δf is the sub-carrier spacing, and τrms is r.m.s delay spread of the channel. The r.m.s delay spread can be expressed as:
                              τ          rms                =                              (                                                                                ∑                    k                                    ⁢                                                            P                      k                                        ⁢                                          τ                      k                      2                                                                                                            ∑                    k                                    ⁢                                      P                    k                                                              -                                                (                                                                                    ∑                        k                                            ⁢                                                                        P                          k                                                ⁢                                                  τ                          k                                                                                                                                    ∑                        k                                            ⁢                                              P                        k                                                                              )                                2                                      )                                              Equation        ⁢                                  ⁢        1        ⁢                  -                ⁢        4            
where Pk and τk denote the k-th path power and delay respectively.                The time domain correlation between two OFDM symbols lm and ln is given byri(lm−ln)=J0(2πTufD(lm−ln))  Equation 1-5where J0, is the zeroth order Bessel function of the first kind, Tu is the OFDM symbol length, and fD is the maximum Doppler frequency given by        
                              f          D                =                              υ            ×                          f              c                                C                                    Equation        ⁢                                  ⁢        1        ⁢                  -                ⁢        6            where υ is the mobile speed, fc is the carrier frequency, and the C is the speed of the light. The zeroth order Bessel function J0 is given by
                                          J            0                    ⁡                      (            x            )                          =                              1            π                    ⁢                                    ∫              0              π                        ⁢                                          cos                ⁡                                  (                                      x                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    θ                                    )                                            ⁢                                                ⅆ                  θ                                .                                                                        Equation        ⁢                                  ⁢        1        ⁢                  -                ⁢        7            
The zeroth order Bessel function J0 can also be expressed as
                                          J            0                    ⁡                      (            x            )                          =                              ∑                          v              =              0                        ∞                    ⁢                                                    (                                                      -                                          x                      2                                                        4                                )                            v                                                      (                                  v                  !                                )                            2                                                          Equation        ⁢                                  ⁢        1        ⁢                  -                ⁢        8            where v!=v(v−1)(v−2) . . . 1. Although J0 is a summation of infinite terms, it can be approximated by finite terms.
Given the received signals ypn of the reference signals spn at the RE indices pn of a transmission link between a transmit point (antenna) and a receive point (antenna)ypn=hpn×spn+npn n=0,1, . . . , Nref−1, [p0, p1, . . . , pNref−1]⊂Ωwhere Nref is the number of reference symbols within estimated region.
The channel estimator 18 finds the channels at all resource elements (REs), ĥ=[ĥ0, ĥ1, . . . , ĥLK−1]T of the transmission link as follows:
                                                        h              ^                        =                          A              ×                                                [                                      B                    +                                                                  1                        SNR                                            ⁢                      I                                                        ]                                                  -                  1                                                                          ︸            G                          ×        z                            Equation        ⁢                                  ⁢        2        ⁢                  -                ⁢        1            
Here:                z contains the least squared channel estimates for reference REs:zn=ypn/spn, n=0,1, . . . , Nref−1.  Equation 2-2        A is the correlation matrix between the channels at all REs and the channels at the reference REs; the size of A is LK by Nref. The (m,n)-th element of A is given by:Am,n=E{hmhpn*}=rf(km−kpn)rl(lm−lpn), m=0,1, . . . , LK−1, n=0,1, . . . , Nref−1.  Equation 2-3        B is the correlation matrix between the channels at the reference REs; the size of B is Nref by Nref. The (m,n)-th element of B is given by:Bm,n=E{hpmhpn*}=rf(kpm−kpn)rl(lpm−lpn), m=0,1, . . . , Nref=1, n=0,1, . . . , Nref−1.  Equation 2-4        
Equation 2-1 shows how the channel estimator 18 calculates the G matrix from the component matrices A and B. Since large matrix inversion is required, this operation is computationally intensive. The calculation of the Bessel function for each element of the matrices is also computationally intensive. Another computationally intensive operation is the multiplication of the G matrix by the LS estimates within Equation 2-1, iethe G×z term. This step needs to be performed at high speed, for each newly received block of input data, ie for each slot (or alternatively: each subframe) in case of LTE and LTE-A UE or base transceiver station (BTS).
Also, the G matrix needs to be updated any time one of the input parameters changes. These parameters include r.m.s delay spread estimate τrms, Maximum Doppler frequency estimate fD, Signal To Noise Ratio and Reference Signal configuration, ie the positions of the Reference Signal within the estimated region.
These complexities limit the use of 2D LMMSE channel estimation in commercial products.
It would be desirable to provide a method and/or device for channel estimation that is more feasible to use within a commercial product and ameliorates one or more of the complexities of known channel estimation methods.
The above discussion of background art is included to explain the context of the present invention. It is not to be taken as an admission or a suggestion that any of the documents or other material referred to was published, known or part of the common general knowledge at the priority date of any one of the claims of this specification.